Transitivity and rotation sets with nonempty interior for homeomorphisms of the $2$-torus

DOI10.1090/S0002-9939-2012-11198-0zbMath1317.37048arXiv1012.0909MaRDI QIDQ2845873

Fabio A. Tal

Publication date: 3 September 2013

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1012.0909

zbMATH Keywords

rotation settorus homeomorphismomega limit

Mathematics Subject Classification ID

Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Rotation numbers and vectors (37E45)

Related Items (5)

Topologically conjugate classifications of the translation actions on low-dimensional compact connected Lie groups ⋮ Bounded and unbounded behavior for area-preserving rational pseudo-rotations ⋮ Ergodicity and annular homeomorphisms of the torus ⋮ A characterization of annularity for area-preserving toral homeomorphisms ⋮ Rotation sets with non-empty interior and transitivity in the universal covering

Cites Work

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• Linearization of conservative toral homeomorphisms
• Generalizations of the Poincaré-Birkhoff theorem
• Homeomorphisms of the annulus with a transitive lift
• Diffeomorphisms having rotation sets with non-empty interior
• On generic rotationless diffeomorphisms of the annulus
• Rotation Sets for Maps of Tori
• Realizing Rotation Vectors for Torus Homeomorphisms
• Rotation sets and ergodic measures for torus homeomorphisms
• Typical Transitivity for Lifts of Rotationless Annulus or Torus Homeomorphisms
• Recurrence and genericity

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